The bilinear transform is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa. The bilinear transform is a special case of a conformal mapping used to convert a transfer function H a of a linear, time-invariant filter in the continuous-time domain to a transfer function H d of a linear, shift-invariant filter in the discrete-time domain, it maps positions on the j ω axis, R e = 0, in the s-plane to the unit circle, | z | = 1, in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linear system and are implementable in the discrete domain by replacing a system's unit delays with first order all-pass filters; the transform preserves stability and maps every point of the frequency response of the continuous-time filter, H a to a corresponding point in the frequency response of the discrete-time filter, H d although to a somewhat different frequency, as shown in the Frequency warping section below.

This means that for every feature that one sees in the frequency response of the analog filter, there is a corresponding feature, with identical gain and phase shift, in the frequency response of the digital filter but at a somewhat different frequency. This is noticeable at low frequencies but is quite evident at frequencies close to the Nyquist frequency; the bilinear transform is a first-order approximation of the natural logarithm function, an exact mapping of the z-plane to the s-plane. When the Laplace transform is performed on a discrete-time signal, the result is the Z transform of the discrete-time sequence with the substitution of z = e s T = e s T / 2 e − s T / 2 ≈ 1 + s T / 2 1 − s T / 2 where T is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation; the above bilinear approximation can be solved for s or a similar approximation for s = ln ⁡ can be performed. The inverse of this mapping is s = 1 T ln ⁡ = 2 T ≈ 2 T

Doreen C. Broadnax, known professionally as Sparky D, or spelled Sparky Dee is an American hip–hop musician and rapper. Broadnax is noted as one of the first female battle rappers, first gaining attention through the Roxanne Wars. Born in Brooklyn, Broadnax was born to African -- American father. Broadnax was raised in the Van Dyke Housing Projects in the Brownsville neighborhood. Broadnax began her music career around 1983 when she became a member of a local hip-hop group, The Playgirls; the group, which consisted of Lisa and Mona recruited Broadnax to join after listening to her rap at a local hangout. After joining the group, The Playgirls recorded "Our Picture of a Man" for Sutra Records in 1983. During her time with the group, Broadnax was introduced to rapper and music producer Spyder D. In 1984, 14–year old rapper Roxanne Shante released "Roxanne's Revenge," a response to U. T. F. O.'s record "Roxanne, Roxanne," a song about a woman who would not respond to their advances. After listening to Shante's song on WBLS' Mr. Magic's Rap Attack on New Year's Eve 1985, Spyder-D decided that Broadnax would respond to Shante's record the following day.

Taking offense to Shante's attack on a fellow Brooklyn crew, Broadnax responded with "Sparky's Turn" under the NIA Records label. The single sold more than 300,000 copies in days of its release becoming certified gold. This, in turn, kicked off the Roxanne Wars, is a well-known series of hip hop rivalries during the mid–1980s, yielding the most answer records in history. In 1985, capitalizing off the success of both records, Roxanne Shante and Broadnax released "Round One, Roxanne Shanté vs Sparky Dee" on Spin Records which included a battle track, in which the two rappers freestyle and diss each other. In subsequent years, Broadnax released a few tracks including d “He’s My DJ” b/w “She’s So Def” with Kool DJ Red Alert in 1985 and "Throwdown" in 1987; the year 1988 saw the release of her first full-length album on B-Boy Records, This is Sparky D’s World. Broadnax continues to stay active in the hip hop community, working with various old school artists on hip hop gospel records including MC Shy D, Spyder D, Roxanne Shante, Kool DJ Red Alert and K Wiz.

Broadnax has stated in interviews that she was a victim of domestic abuse, struggled with a crack cocaine addiction and was involved in prostitution sometime after the height of her career. In 2017, Broadnax was portrayed by Cheryse Dyllan in Netflix film Roxanne, Roxanne, a biopic about the life of Roxanne Shante

Elias Selah Holliday was a U. S. Representative from Indiana. Born in Aurora, Holliday spent the early part of his life on farms in Indiana and Iowa, he taught in the public schools in Iowa. During the Civil War enlisted in the Fifth Kansas Regiment and served until August 12, 1864, when he was mustered out with the rank of first sergeant, he attended Bartholomew County, Indiana. He engaged in teaching in Indiana, he studied law at Indiana. He commenced practice in Carbon, Indiana, he moved to Brazil, Indiana, in 1874. He served as mayor of Brazil 1877-1880, 1887, 1888. City attorney in 1884, he served as member of the city council 1892-1896. Holliday was elected as a Republican to the three succeeding Congresses, he was not a candidate for renomination in 1908. Reengaged in the practice of law in Brazil until 1922, he died in Brazil, March 13, 1936. He was interred in Cottage Hill Cemetery. United States Congress. "Elias S. Holliday". Biographical Directory of the United States Congress; this article incorporates public domain material from the Biographical Directory of the United States Congress website http://bioguide.congress.gov

The order of battle of the Serbian Army in the First Balkan War is a list of the Serbian units that fought the major campaigns against the Ottoman army from October 1912 to May 1913. Apart from the infantry divisions of the Serbian army, one Bulgarian infantry division was part of it. Under the command of Crown Prince Alexander Karađorđević. Chief of Staff: Colonel Petar Bojović. Commander: General Stepa Stepanović Commander: General Božidar Janković Commander: General Mihailo Živković Commander: Colonel Milivoje Anđelković III supernumerary infantry regiment IV infantry regiment - LtCol Vilotije Marković 3rd battery 4th mountain battery 1st Užice position battery 6th heavy battery 120 mm cavalry squadron First Balkan war Kingdom of Serbia A.^ In the Royal Serbian Army and cavalry divisions were units of battalion size not to be confused with the higher level of divisions which had geographic names. Each of them was made of three regional regimental commands with four battalion districts each.

Each divisional area provided one first-call division, one second-call division, one or two cavalry squadrons and 6 station batteries. Belgrade Istoriski institut Jugoslovenske narodne armije; the First Balkan War, 1912-1913: Serbian Army Operations. Savo Skoko. Vojvoda Stepa Stepanović in the wars of Serbia: 1876-1918. Beogradski izdavačko-grafički zavod. Borislav Ratkovic. Mobilization of the Serbian Army for the First Balkan War, October 1912. Kiraly and Djordjevic, East Central Europe

Lake Orta is a lake in northern Italy, west of Lake Maggiore. It has been so named since the 16th century, but was called the Lago di San Giulio, after Saint Julius, the patron saint of the region, its southern end is about 35 kilometres by rail, to the northwest of Novara on the main Turin-Milan line, while its north end is about 6 kilometres by rail south of the Gravellona-Toce railway station, halfway between Ornavasso and Omegna. Its scenery is characteristically Italian, while the San Giulio island has some picturesque buildings, takes its name from the local saint, who lived in the 4th century. Located around the lake are Orta San Giulio, built on a peninsula projecting from the east shore of the lake, Omegna at its northern extremity, Pettenasco to the east, Pella to the west, it is supposed that the lake is the remnant of a much larger sheet of water by which the waters of the Toce flowed south towards Novara. As the glaciers retreated the waters flowing from them reduced, were diverted into Lake Maggiore.

The inaugural European Rowing Championships were held on Lake Orta in 1893. A frequent ferry service connects villages around the lake; this article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed.. "Orta, Lake of". Encyclopædia Britannica. Cambridge University Press. CNR - ISE: Laghi LIMNO Banca dati dei laghi italiani: Orta Lake Orta at World lake database Media related to Lago d'Orta at Wikimedia Commons Orta.net Pictures and curiosities about lake of Orta

Highways England traffic officers perform a functional role within Highways England. In April 2004, Highways Agency traffic officers began working alongside police on motorways in the West Midlands; the national roll-out of traffic officers was completed on 18 July 2006, they now cover all of the motorway network within England, i.e. that, owned or managed by Highways England, some of the all-purpose trunk road network. On 1 April 2015 the Highways Agency became a government-owned company. Traffic operations play a significant role in achieving Highways England's three imperatives of safety, customer service and delivery. Traffic officers help to keep road users safe, they provide customer service every day of the year and assist with the delivery of schemes and projects, providing key services such as rolling road block. This is achieved through the planning and delivery of operational services, the function undertaken by on-road traffic officers, the management of the network from Highway England's control centres, the services Highways England supplies to the public, its national incident liaison role.

This aim is underpinned by legislative and regulatory requirements, the Network Operations Partnership Agreement and the National Guidance Framework agreed with the National Police Chiefs' Council. While patrols were always crewed by two traffic officers, following a successful trial in 2013, all traffic officers are to be trained in the near future to operate singly crewed, increasing the potential reach of the service. Traffic officers wear high-visibility jackets, distinctive by yellow markings. All staff who work on the network are required to wear protective equipment such as safety boots and safety goggles. Staff have the option to wear a white collared shirt and tie, an open necked white shirt or a navy collared polo shirt. All officers carry a portable Airwave radio. Traffic officers patrol the motorway network and all-purpose trunk roads in high-visibility patrol vehicles that feature black and yellow Battenburg livery, amber and rear red facing lighting; the vehicles have all wheel drive capability and are used to assist in the management of incidents and where appropriate clear broken-down or disabled vehicles to a place of safety off the carriageway.

The vehicles can operate in severe weather and carry equipment including emergency traffic management kits and other specialised equipment required to safely remove vehicles and deal with a range of different incidents they may encounter when on patrol. The combination of the vehicle size and ancillary lighting enhances their visibility when positioned at an incident, they are fitted with Airwave radio hands-free mobile telephone, alternating flashing headlights and a bull horn to assist with progressing through stationary traffic on approach to an incident. They have variable message signs at the rear; when travelling on the hard shoulder, vehicles use front- and rear-facing amber lighting, are restricted to 20 mph. When stationary on the hard shoulder, vehicles illuminate rear-facing amber LEDs. However, when the vehicle is working in the carriageway all the rear-facing lights are displayed to warn approaching traffic. Traffic officers, unlike police, must comply with all speed limits, including temporary mandatory limits in roadworks.

While stationary on the hard shoulder and if a traffic officer feels it is necessary - because of the weather or location - they may use the red rear lights, in addition to the amber lights. This will be noted in the traffic officer's pocket notebook as a dynamic risk assessment and relayed to a regional control centre for entry on to the log; the traffic officers use different models of 4x4 vehicles, all diesel-powered with automatic transmissions. Vehicles used for patrolling as of 2018 include Land Rover Mitsubishi Shogun models. Traffic officers maintain contact with each other and the regional operational control centres by use of Sepura hand-held and vehicle TETRA radios using the Airwave network, enabling officers to co-ordinate with other Airwave users; each patrol vehicle is fitted with a hands-free mobile phone. Traffic officers attend incidents ranging from breakdowns and road debris to serious road traffic collisions taking the lead command role, except where there is an incident involving loss of life, life-changing injuries or potential criminal activity.

Traffic officers patrol 3,565 miles of the road network, in 2017 the total number of incidents attended was 230,122. Traffic officers principally derive powers from the Traffic Management Act 2004 and have jurisdiction over the strategic road network of England, under authorisation given by the secretary of state. Traffic officers comply with the directions of a police constable, to exercise their powers must be on duty and in uniform. For the purposes of: maintaining or improving the movement of traffic on a relevant road over which the traffic officer has jurisdiction preventing or reducing the effect of anything causing congestion or other disruption to the movement of traffic on such a road avoiding danger to persons or other traffic using such a road preventing damage to, or to anything on or near, such a roada traffic officer may: direct a person driving or propelling a vehicle to stop the vehicle, or to make it proceed in, or keep to, a particular line of traffic for the purposes of a traffic survey of any description, being carried out on or in the vicinity of a road, to direct a person driving or propelling a vehicle to stop the vehicle, or to make it proceed in, or keep to, a particular line of traffic, or to proceed